Author: admin
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Scatchard-Hildebrand Theory
Returning to Eqn. 12.10, G. Scatchard in Europe and Joel H. Hildebrand in the United States both made similar adjustments to match the van der Waals equation to experiment and provide a model capable of predictions for nonpolar fluids. They made an assumption that is equivalent to assuming k12 = 0 in Eqn. 12.4. Setting , and collecting terms, J.H.…
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The van Laar Model
Johannes van Laar found that the parameters from the van der Waals equation of state were not accurate in predicting excess energy of mixing, and empirical fitting was required. He simplified the equation for the excess internal energy by arbitrarily defining a single symbol, “Q,” to represent the final term in the equation: J. van…
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The van der Waals Perspective for Mixtures
Empirical models like the Redlich-Kister expansion provide a significant improvement over the ideal solution approximation, but they lack the kind of connection with the molecular perspective that we have developed in Chapters 1 and 7. The empirical models of Chapter 11 are useful for determining the activity coefficients from a given expression for GE, but they suggest little about the form…
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Homework Problems
11.1. The volume change on mixing for the liquid methyl formate(1) + liquid ethanol(2) system at 298.15 K may be approximately represented by J. Polack, Lu, B.C.-Y. 1972. J. Chem Thermodynamics, 4:469: ΔVmix = 0.8x1x2 cm3/mol a. Using this correlation, and the data V1 = 67.28 cm3/mol, V2 = 58.68 cm3/mol, determine the molar volume of mixtures at x1 = 0, 0.2, 0.4, 0.6, 0.8, 1.0…
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Practice Problems
P11.1. Ninov et al. (J. Chem. Eng. Data, 40:199, 1995) have shown that the system diethylamine(1) + chloroform(2) forms an azeotrope at 1 bar, 341.55 K and x1 = 0.4475. Is this a maximum boiling or minimum boiling azeotrope? Determine the bubble temperature and vapor composition at x1 = 0.80 and 1 bar. (ANS. 331 K, 0.97) P11.2. Derive the expression…
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Fitting Activity Models to Multiple Data
Fitting of the Margules equations to limited data has been discussed in Examples 11.2 and 11.5. Fits to multiple points are preferred, which requires regression of the parameters to optimize the fit. In a few cases, the Gibbs excess function can be rearranged to form the basis for a linear regression. In general, a non-linear regression may be…
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Preliminary Indications of VLLE
Recall from Section 10.7 that azeotropes occur at x=y, where a maximum or minimum appears in all the plots. Also note that the bubble and dew lines do not cross, but they touch at the azeotrope composition. Occasionally when a P-x-y or T-x-y diagram is generated in a Stage III calculation, the diagram can look very odd. The two-parameter fit in Fig. 11.5 was…
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Activity Coefficients at Special Compositions
Two parameter models provide sufficient flexibility with a balance of relative simplicity to provide successful VLE modeling. Determination of activity for each component permits two parameters to be fitted, and special compositions can be used. Azeotropes The location of an azeotrope is very important for distillation design because it represents a point at which further…
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Redlich-Kister and the Two-Parameter Margules Models
We noted in Example 11.1 a shortcoming in the one-parameter model’s representation of the skewness of experimental excess Gibbs energy. In principle, adjusting both the magnitude and skewness of GE is possible with a two-parameter model equation. The mathematical relations in Sections 11.3–11.5 liberate us to conjecture freely about forms of GE that may fit any given set of VLE data. Based on…
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Modified Raoult’s Law and Excess Gibbs Energy
The excess Gibbs energy is Excess Gibbs energy. where we have added and subtracted the sum of the component Gibbs energies in the second line, and used Eqns. 10.65 and 10.66 in the last line. Let us further examine . Recall that , (Eqn. 10.42). Previously in Eqn. 10.48 we expressed μi relative to a pure component value using a ratio of fugacities. Generalization…